Actually, such a document--a first-century work, associated with a disciple of Jesus, who was an eye-witness to the events described in the book, which in many ways reinforces the portrait of Jesus in the Synoptic Gospels--already exists... it's called the "Gospel of John"!
I stole the idea for this post from Mark Allan Powell who has contributed an exciting essay to John, Jesus and History: Volume 1, Critical Appraisals of the Critical Views (SBL Symposium Series; ed. P. N. Anderson, F. Just, and T. Thatcher; Atlanta: Society of Biblical Literature, 2008), entitled, "The De-Johannification of Jesus."
In the concluding paragraph he offers this provocative thought:
"If John's Gospel had not made it into the canon, if it had been lost to history only to be discovered now, the impact on historical Jesus studies would be revolutionary. Imagine! A book on the life and teachings of Jesus that is almost as early as the Synoptic Gospels, that claims to be based in part on eye-witness testimony, that contains some material that is almost certainly very primitive, that may very well be independent of the other Gospels while corroborating what they say at many points, and that offers what is ultimately a rather different (although not wholly incompatible) spin on the Jesus story. The implications of such a discovery would be phenomenal: every work previously written on the historical Jesus would be deemed obsolete and the full attention of scholarship would turn toward discovering what this alternative tradition had to offer. Of course, nothing like this has occurred, but many scholars seem to be saying, "we do have such a book; perhaps we should not ignore it."